"Friendship" is a noun, meaning the state of being friends.
If you are looking for a verb related to the concept of friendship, you could use:
* Befriend: To become friends with someone.
* Friend: To become friends with someone (less formal).
* Bond: To form a strong connection with someone.
* Connect: To establish a relationship with someone.
Let me know if you had something else in mind, and I can help further!